Question

phân tích đa thức thành nhân tử

a. \(x^2-6x+9-9y^2\)

b.\(x^3-3x^2+3x-1+2\left(x^2-x\right)\)

c. \(5x^2-45y^2-30y-5\)

d. \(x^2+9x+20\)

e. \(6x^2-11x-10\)

g. x\(x^3+9x^2+23x+15\)

Answer 1

a) \(x^2-6x+9-9y^2=x^2-2\cdot3+3^2-\left(3y\right)^2=\left(x-3\right)^2-\left(3y\right)^2=\left(x-3-3y\right)\cdot\left(x-3+3y\right)\)

Answer 2

b) \(x^3-3x^2+2x-1+2\cdot\left(x^2-x\right)=\left(x-1\right)^3+2x\cdot\left(x-1\right)=\left(x-1\right)\cdot\left[\left(x-1\right)^2+2x\right]\)

Answer 3

c) \(5x^2-45y^2-30y-5=5\cdot\left(x^2-9y^2-6y-1\right)=5\cdot\left\{x^2-\left[\left(3y\right)^2+2\cdot3y\cdot1+1^2\right]\right\}=5\cdot\left[x^2-\left(3y+1\right)^2\right]=5\cdot\left(x-3y-1\right)\cdot\left(x+3y+1\right)\)

Answer 4

d) \(x^2+9x+20=x^2+5x+4x+20=x\cdot\left(x+5\right)+4\cdot\left(x+5\right)=\left(x+5\right)\cdot\left(x+4\right)\)